Adaptive Backstepping Decoupled Fast Terminal Sliding Mode Control for Underactuated Systems Under Uncertainties and Actuator Faults

This paper presents an Adaptive Backstepping Decoupled Fast Terminal Sliding Mode Control (ABDFTSMC) framework for underactuated nonlinear systems with coupled dynamics. Traditional sliding mode control methods often suffer from chattering, reliance on conservative uncertainty bounds, and inefficiency in managing underactuation. The proposed framework integrates adaptive backstepping with a decoupling mechanism and fast terminal sliding mode control to ensure finite-time convergence and enhance resilience to uncertainties and actuator faults. Using a recursive Lyapunov-based design, the controller dynamically estimates and compensates for uncertainties and actuator faults without requiring prior knowledge of disturbance bounds. A hierarchical decoupling strategy stabilizes subsystems, reducing control complexity while maintaining precise tracking. Experimental validation on an inverted pendulum-cart system demonstrates the effectiveness of the framework, showing significant reductions in chattering under nominal conditions. When subjected to disturbances—including a 25% loss in actuator effectiveness, additive faults, and parametric uncertainties—the proposed controller achieved superior tracking performance with a settling time of 4.73 seconds, outperforming conventional sliding mode controls, which failed to stabilize the system under the same conditions.